When it comes to Google Analytics this is probably my favorite thing to watch yet also possibly the least useful. Real Time Analytics will tell you how many people are on at that exact time, what pages they are viewing, how long they have been on, and how they got to the site. It's pretty incredible. I'm also a map guy and love the map that is displayed letting you see where people are logging in from displayed on a map.
You get to Real Time Analytics from the Home Screen Going to Standard Reports --> choosing Real Time --> then choose Overview and you are there. You can then browse around and check out the incredible reports that Google pulls together in real time!
While most of my viewing of this page can be an ineffective use of time and just fun to watch, it also can provide great value. When posting at specific times or publicity events that you think might drive increased traffic are good times to monitor Real Time Analytics.
If you have some uses for this tool, I would love to hear them! Even if you don't I think you too will enjoy watching your web traffic and their behavior in real time via Real Time Reporting. Enjoy!